There is a square field of 10m×10m which is divided into 100 squared blocks. Each block can either contain wheat field or corn field. What is the maximum number of corn fields possible such that no two corn fields share an edge?

Question

Accepted Answer

The maximum number of corn fields possible in a 10m×10m square field without sharing edges is 25.

The maximum number of corn fields is achieved by placing them in a diagonal pattern across the field.
Each corn field will have 4 wheat fields surrounding it to ensure no two corn fields share an edge.
The total number of corn fields possible in this arrangement is 25.

Accepted Answer

Suppose the dimensions are n*n 
f(n) = n + f(n-1) if n is odd
f(n) = n-1 + f(n-1) if n is even
solving this sequence
f(1)=1

if n is even: f(n) = (n^2)/2
if n is odd: f(n) =( 1 + n^2 )/2

Gives the ans f(10) = 50

Accepted Answer

placing alternatively will result in answer 50

Accepted Answer

since 'no two corn field share the edge' and not mentions about wheat for the constraint answer would be 52

Accepted Answer

50 is the correct answer

There is a square field of 10m×10m which is divided into 100 squared blocks. Each block can either contain wheat field or corn field. What is the maximum number of corn fields possible such that no two corn fields share an edge?

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